Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Analogue of the degree conjecture over function fields


Author: Mihran Papikian
Journal: Trans. Amer. Math. Soc. 359 (2007), 3483-3503
MSC (2000): Primary 11G05; Secondary 11G18
Published electronically: February 13, 2007
MathSciNet review: 2299464
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Abstract: Under a certain assumption, similar to Manin's conjecture, we prove an upper bound on the degree of modular parametrizations of elliptic curves by Drinfeld modular curves, which is the function field analogue of the conjectured bound over the rational numbers.


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Additional Information

Mihran Papikian
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
Email: papikian@math.stanford.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04147-5
Keywords: Degree conjecture, Drinfeld modular curves, ABC conjecture, monodromy pairing
Received by editor(s): October 27, 2004
Received by editor(s) in revised form: July 26, 2005
Published electronically: February 13, 2007
Additional Notes: This research was supported by a fellowship from the European Postdoctoral Institute
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.